My intention with this blog is to share some of the more interesting curiosities of math. Often in the form of mathematical puzzles, riddles or paradoxes. Some can be applied to the real world, showing that all is not always what it seems. I'll include a calculation now and then but will keep it light — heck I'm far from a math wizz myself.

Monday, February 28, 2011

What is the highest number there is? Let's try and find out by working our way up. To save myself from having to write down a lot of digits, let me first explain the scientific notation:

1 × 102 = 1 × 10 × 10 = 100

1 × 103 = 1 × 10 × 10 × 10 = 1000

1 × 104 = 1 × 10 × 10 × 10 × 10 = 10000

Basically, powers of 10 can be used to define the number of zeros that follow the ‘1’. So here's some large numbers you might know: a million, a billion, a trillion, a quadrillion... These can be written respectively as 106, 109, 1012 and 1015. You might knew these first few, but that list actually goes on for a while. Take for example a vigintillion, which is 1063. Are there any higher?

Of course! How about the googol? It is notated as 10100. That's a ‘1’ with a hundred zeros! Is this the largest number? Nah, we can put at least the centillion (10303), septuagintacentillion (10513) and the millinillion (103003) on the table.

We need to do better than this, so let's push it into crazy territory. A googolplex is 10googol — yes, that's 10 to the power of a googol. A ‘1’ with a googol zeros. 1010100. Fine! It is a 1 with 10 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 zeros. So as you can see I just wrote out a googol. I cannot write out a googolplex: there is not enough room in our universe to do so. See, the number of atoms in the observable universe is estimated to be around 1080. This means that writing down a googolplex requires far more zeros than there are atoms in the universe!